purpose of this design
assignment
was to implement and simulate both state space
and transfer function descriptions
of a set
of
linearized differential
equations
that model
Modeling and Discrete-Logic Control
of a Quadruple-Tank
System
Bryan Guner
1
and Sean Fernandez
1
; Advisor: Dr.
Ambrose Adegbege
1
1
Department of Electrical
and Computer Engineering, The College of New Jersey,
Ewing, NJ
The aforementioned
quadruple tank
system
consists of
four
water tanks
and two
pumps
that form
a
two-input
two-output system.
The
intention is to
control the
level of the water in the bottom
two tanks while
the
pumps delivers
water to
the top
two tanks
that trickle
down into
the
bottom
two via
two outlets
situated at
the bottom
of the top
two tanks.
The inputs
are
the control
voltages sent
to the
pumps
and the
outputs are
the
sensor
voltages
corresponding
to the water
levels in
the lower
tanks. A
mathematical model
is
developed using
a combination
of the
mass
balance equation,
Bernoulli’s
equation and
the derived
flow
coefficient taking
into account
the
proportionality
splitting
in the pump
system.
The system
is first
modeled
by a
set
of nonlinear
differential
equations which are
then linearized
about an
operating point
that
is comprised
of a water level height argument
and the voltage
to the pumps.
Design/Methods
Conclusion
.
Results
The goal of this design
assignment was
to develop
and
simulate a
mathematical model
of a
quadruple-tanks system
and
subsequently implement discrete-logic control using
the LabVIEW
software package.
The purpose
was
to exercise
our knowledge
of the
differential equations that
represent such
a system,
and to
convert
them into
linearized state-space and
transfer function
descriptions that
could be more easily used
to simulate
said system
in LabVIEW.
Nonlinear Model sub-VI:
LabVIEW Implementation:
Linearized
State-Space Model sub-
VI:
Linearized
Transfer Function Model
sub-VI:
Schematic
of 4 Tank
System:
Linear Equations:Nonlinear
Equations:
State-Space Configuration:
Transfer Function
Configuration:
Quadruple Tank-System
Block Diagram:
Output Water Levels Front Panel:
• Purpose was to implement and simulate both state
space and transfer
function to model behavior
of
system
• Valuable learning experience
in linearization
of
discrete control of systems
• Overall, students
successfully modeled a quadruple-
tank system
utilizing LabVIEW
• Learned about the
use of
subVI’s to reduce
complexity and size of
code
• Close approximation
to working experience
of a
control systems engineer
Introduction
Abstract